The sample mean for a recent introductory psychology test was 78,and the sample variance was 9.If a student's z-score = -2.0,what was this student's raw test score?

Question

Quizplus · Accepted Answer

We can use the formula for z-score:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the population mean, and σ is the population standard deviation (or sample standard deviation if n is large).

We are given that the sample mean is 78, so μ = 78. We are also given the sample variance, which is the square of the sample standard deviation, so s^2 = 9 => s = 3. Since the sample size is not given, we assume that it is large enough for us to use s as an estimate of σ.

We are given that z = -2.0, so we can plug in the values:
-2.0 = (x - 78) / 3
Solving for x, we get:
x = 78 - 2.0(3)
x = 72

Therefore, the student's raw test score was 72.

The Sample Mean for a Recent Introductory Psychology Test Was